MoorePenrose< Blackbox > Class Template Reference

Generalized inverse of a blackbox. More...

#include <moore-penrose.h>

Inheritance diagram for MoorePenrose< Blackbox >:

Data Structures
struct	rebind

Public Types
typedef Blackbox::Field	Field
typedef Blackbox::Element	Element

Public Member Functions
	MoorePenrose (const Blackbox *A, size_t rank)
	Constructor from field and dense vector of field elements.
	MoorePenrose (const MoorePenrose &A)
	Copy constructor.
	~MoorePenrose ()
	Destructor.
template<class OutVector, class InVector>
OutVector &	apply (OutVector &y, const InVector &x) const
	Application of BlackBox matrix.
template<class OutVector, class InVector>
OutVector &	applyTranspose (OutVector &y, const InVector &x) const
	Application of BlackBox matrix transpose.
size_t	rowdim (void) const
	Retreive _row dimensions of BlackBox matrix.
size_t	coldim (void) const
	Retreive _column dimensions of BlackBox matrix.
const Field &	field ()

Detailed Description

template<class Blackbox>
class LinBox::MoorePenrose< Blackbox >

Generalized inverse of a blackbox.

Efficiency concerns when many applications are used.

Given an arbitrary matrix in black box representation, this black box represents the Moore-Penrose inverse of the matrix.

This implementation assumes that A already has a nonsingular principal r x r minor. It is the caller's responsibility to ensure that that condition holds.

Given MoorePenrose M(A, r), and vector b, we have that M.apply(u, b) provides the least norm, least squares solution x = u to Ax = b.

TODO: remove the requirement that lpm is nonsingular. Specialize for dense matrices.

Member Typedef Documentation

Field

template<class Blackbox>

typedef Blackbox::Field Field

Element

template<class Blackbox>

typedef Blackbox::Element Element

Constructor & Destructor Documentation

MoorePenrose() [1/2]

template<class Blackbox>

MoorePenrose ( const Blackbox * A, size_t rank )

inline

Constructor from field and dense vector of field elements.

-param BB Black box from which to extract the submatrix -param row First row of the submatrix to extract (1.._BB->rowdim ()) -param col First column of the submatrix to extract (1.._BB->coldim ()) -param rowdim Row dimension -param coldim Column dimension

Parameters

A
rank

MoorePenrose() [2/2]

template<class Blackbox>

MoorePenrose ( const MoorePenrose< Blackbox > & A )

inline

Copy constructor.

Bug

Value of pointer '_matB1', which points to allocated memory, is copied in copy constructor instead of allocating new memory.

~MoorePenrose()

template<class Blackbox>

~MoorePenrose ( )

inline

Destructor.

Member Function Documentation

apply()

template<class Blackbox>

template<class OutVector, class InVector>

OutVector & apply ( OutVector & y, const InVector & x ) const

inline

Application of BlackBox matrix.

y= A*x. Requires one vector conforming to the LinBox vector archetype. Required by abstract base class.

Returns

reference to vector y containing output.

Parameters

x	constant reference to vector to contain input
y

applyTranspose()

template<class Blackbox>

template<class OutVector, class InVector>

OutVector & applyTranspose ( OutVector & y, const InVector & x ) const

inline

Application of BlackBox matrix transpose.

y= transpose(A)*x. Requires one vector conforming to the LinBox vector archetype. Required by abstract base class.

Returns

reference to vector y containing output.

Parameters

x	constant reference to vector to contain input
y

rowdim()

template<class Blackbox>

size_t rowdim ( void ) const

inline

Retreive _row dimensions of BlackBox matrix.

This may be needed for applying preconditioners. Required by abstract base class.

Returns

integer number of _rows of black box matrix.

coldim()

template<class Blackbox>

size_t coldim ( void ) const

inline

Retreive _column dimensions of BlackBox matrix.

Required by abstract base class.

Returns

integer number of _columns of black box matrix.

field()

template<class Blackbox>

const Field & field ( )

inline

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The documentation for this class was generated from the following file:

• moore-penrose.h